Metalens collimators and condensers

ABSTRACT

According to various embodiments, a device may include a light-emitting diode (LED) to generate optical radiation at an operational wavelength with a divergent emission profile, such as a Lambertian emission profile, relative to a planar face thereof. A metalens may be positioned to modify the divergent emission profile of the optical radiation from the LED to have a modified transmission profile. The metalens may comprise, for example, a substrate and a two-dimensional array of passive pillars that extend from the substrate with a radially symmetric pattern of varying pillar diameters. The pillars may be spaced from one another according to a uniform subwavelength interelement spacing. The diameters of the pillars are selected as a function of the operational wavelength to provide a target phase gradient that modifies the divergent emission profile of the optical radiation from the LED to have the modified transmission profile.

PRIORITY APPLICATIONS

This application claims benefit under 35 U.S.C. § 119 and priority toU.S. Provisional Patent Application No. 63/371,608 filed on Aug. 16,2022, titled “Single-Element Metalens Collimators and Condensers,” whichapplication is hereby incorporated by reference in its entirety.

TECHNICAL FIELD

This disclosure relates to optical metamaterials. More specifically,this disclosure relates to transmissive optical metasurfaces andmetalenses.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1A illustrates an example of a light-emitting diode (LED) with areflector and aspherical lens, according to one embodiment.

FIG. 1B illustrates a two-dimensional array of LEDs with asphericallenses, according to one embodiment.

FIG. 2A illustrates a top-down view of an example representation of apattern of deflector elements for a metalens structure, according to oneembodiment.

FIG. 2B illustrates an enlarged perspective view of the examplerepresentation of the pattern of deflector elements in the metalens ofFIG. 2A, according to one embodiment.

FIG. 3A illustrates an example block diagram of a side view of ametalens with nanopillar deflectors positioned on a substrate totransmissively steer incident optical radiation, according to oneembodiment.

FIG. 3B illustrates a metalens with a radially symmetric pattern ofpillar diameters to focus optical radiation, according to oneembodiment.

FIG. 3C illustrates an example block diagram of a metalens concentratorand condenser for an LED source, according to one embodiment.

FIG. 4A illustrates an example of a unit cell of a transmissivemetasurface for red optical radiation, according to one embodiment.

FIG. 4B illustrates a graph of the transmission efficiency of redoptical radiation for pillars having various radii, according to oneembodiment.

FIG. 4C illustrates a graph of the phase shift of red optical radiationassociated with pillars having various radii, according to oneembodiment.

FIG. 4D illustrates a finite-difference time-domain (FDTD) simulation ofa metalens with a radially symmetric pattern of pillar diametersfocusing red optical radiation, according to one embodiment.

FIG. 5A illustrates an example of a unit cell of a transmissivemetasurface for green optical radiation, according to one embodiment.

FIG. 5B illustrates a graph of the transmission efficiency of greenoptical radiation for pillars having various radii, according to oneembodiment.

FIG. 5C illustrates a graph of the phase shift of green opticalradiation associated with pillars having various radii, according to oneembodiment.

FIG. 5D illustrates an FDTD simulation of a metalens with a radiallysymmetric pattern of pillar diameters focusing green optical radiation,according to one embodiment.

FIG. 6A illustrates an example of a unit cell of a transmissivemetasurface for blue optical radiation, according to one embodiment.

FIG. 6B illustrates a graph of the transmission efficiency of blueoptical radiation for pillars having various radii, according to oneembodiment.

FIG. 6C illustrates a graph of the phase shift of blue optical radiationassociated with pillars having various radii, according to oneembodiment.

FIG. 6D illustrates an FDTD simulation of a metalens with a radiallysymmetric pattern of pillar diameters focusing blue optical radiation,according to one embodiment.

FIG. 7A illustrates a condenser metalens of titanium dioxide pillarsmounted to an LED, according to one embodiment.

FIG. 7B illustrates an FDTD simulation of a titanium dioxideconcentrator metalens mounted on a red LED, according to one embodiment.

FIG. 7C illustrates a two-dimensional representation of the operation ofa free space collimator metalens evaluated with red laser light,according to one embodiment.

FIG. 7D illustrates a graph of the intensity of the free spacecollimator metalens of FIG. 7C, according to one embodiment.

FIG. 7E illustrates a two-dimensional representation of the operation ofa free space collimator metalens evaluated with red laser light passedthrough a beam expander, according to one embodiment.

FIG. 7F illustrates a graph of the intensity of the free spacecollimator metalens of FIG. 7E, according to one embodiment.

FIG. 7G illustrates an FDTD simulation of a titanium dioxideconcentrator metalens mounted on a green LED, according to oneembodiment.

FIG. 7H illustrates an FDTD simulation of a titanium dioxideconcentrator metalens mounted on a blue LED, according to oneembodiment.

FIG. 8A illustrates a condenser metalens of polysilicon pillars mountedto an LED, according to one embodiment.

FIG. 8B illustrates an example of a unit cell of a polysiliconconcentrator metalens for red optical radiation, according to oneembodiment.

FIG. 8C illustrates a graph of the transmission efficiency of redoptical radiation for polysilicon pillars having various radii,according to one embodiment.

FIG. 8D illustrates a graph of the phase shift of red optical radiationassociated with polysilicon pillars having various radii, according toone embodiment.

FIG. 8E illustrates an FDTD simulation of concentrated red opticalradiation by a metalens with polysilicon pillars mounted to a red LED,according to one embodiment.

FIG. 8F illustrates an example of a unit cell of a polysiliconconcentrator metalens for green optical radiation, according to oneembodiment.

FIG. 8G illustrates a graph of the transmission efficiency of greenoptical radiation for polysilicon pillars having various radii,according to one embodiment.

FIG. 8H illustrates a graph of the phase shift of green opticalradiation associated with polysilicon pillars having various radii,according to one embodiment.

FIG. 8I illustrates an FDTD simulation of concentrated green opticalradiation by a metalens with polysilicon pillars mounted to a green LED,according to one embodiment.

FIG. 8J illustrates an example of a unit cell of a polysiliconconcentrator metalens for blue optical radiation, according to oneembodiment.

FIG. 8K illustrates a graph of the transmission efficiency of blueoptical radiation for polysilicon pillars having various radii,according to one embodiment.

FIG. 8L illustrates a graph of the phase shift of blue optical radiationassociated with polysilicon pillars having various radii, according toone embodiment.

FIG. 8M illustrates an FDTD simulation of concentrated blue opticalradiation by a metalens with polysilicon pillars mounted to a blue LED,according to one embodiment.

FIG. 9A illustrates an example corrector metalens with a radiallysymmetric pattern of pillar diameters, according to one embodiment.

FIG. 9B illustrates a graph of the energy focus for red opticalradiation using titanium dioxide pillars, according to one embodiment.

FIG. 9C illustrates a graph of the energy focus for red opticalradiation using polysilicon pillars, according to one embodiment.

FIG. 10A illustrates a block diagram of an LED with a Lambertianemission profile, according to one embodiment.

FIG. 10B illustrates a block diagram of an LED with a metalensconfigured to collimate and/or condense the optical radiation from theLED into a target emission profile, according to one embodiment.

FIG. 11A illustrates a block diagram of a metalens for an LED, accordingto one embodiment.

FIG. 11B illustrates geometric calculations associated with the metalensof FIG. 11A, according to one embodiment.

FIG. 11C illustrates a table of example metasurface radius valuescalculated for various angles of divergence values for an LED, accordingto one embodiment.

FIG. 12A illustrates a block diagram of an inverted metalens for an LED,according to one embodiment.

FIG. 12B illustrates geometric calculations associated with the invertedmetalens of FIG. 12A, according to one embodiment.

FIG. 12C illustrates a table of example inverted metasurface radiusvalues calculated for various angles of divergence values for an LED,according to one embodiment.

FIG. 13A illustrates a block diagram of an LED with an inverted metalensapplied to an LED surface, according to one embodiment.

FIG. 13B illustrates a two-dimensional array of LEDs with invertedmetalenses, according to one embodiment.

FIG. 14A illustrates a block diagram of an LED with an inverted metalenswith a matched aperture applied to an LED surface, according to oneembodiment.

FIG. 14B illustrates a two-dimensional array of LEDs withmatched-aperture inverted metalenses, according to one embodiment.

FIGS. 15A-D illustrate images of the arrays of pillars forming ametalens captured using an electronic microscope at varying levels ofmagnification, according to various embodiments.

DETAILED DESCRIPTION

Various embodiments, systems, apparatuses, and methods are describedherein that relate to condensing, concentrating, and collimating opticalradiation generated by a light-emitting diode. Many electronic displaysand other imaging technologies utilize multi-pixel LED arrays togenerate optical radiation at various wavelengths (e.g., differentvisible colors of light) using at least three different colors of LEDsubpixels (e.g., red, green, and blue subpixels for an RGB display). Insome embodiments, a single LED (e.g., a monochrome LED) may be used asthe illumination source for a display (e.g., as a backlight).Traditional glass or plastic optics may be used to condense,concentrate, and/or collimate the optical radiation generated by themonochrome LED. Examples of traditional optics include lenses that arerelatively large (e.g., thick) and have relatively long minimum focallengths. In fact, thicker lenses are generally required to attainshorter focal lengths. Traditional optics result in an LED andmulti-element lens assembly that is several centimeters thick. Even morerecent developments utilizing microlens arrays either have a thicknessin excess of a few millimeters (or even centimeters) and/or theireffective focal lengths are relatively long (e.g., several millimetersor even centimeters).

Moreover, traditional optical elements scatter and absorb some of thelight, resulting in optical transmission efficiencies that are less thanoptimal or desirable. Additionally, traditional optics are far lessefficient with incoherent light and light originating from a source witha large angular spread (e.g., an LED source) as compared to coherentlight from a laser source.

This disclosure describes several embodiments and variations ofmetalenses formed as an array of pillars having subwavelength dimensions(e.g., radii, lengths, widths, and/or heights) and sub-wavelengthinterelement spacings (e.g., the spacing between adjacent pillars in agiven metalens is less than an operational wavelength). The metalensesdescribed herein allow for LED assemblies with reduced thickness, highconcentration efficiencies, and cost-effective mass production. Asdescribed herein, the pillars or nanopillars may be manufactured usingtitanium dioxide, polysilicon, silicon nitride, amorphous silicon,silicon rich nitride, hydrogenated silicon rich silicon nitride, and/orhydrogenated amorphous silicon (a-H-Silicon).

As described herein, a substrate surface may be configured as atransmissive surface to allow optical radiation to pass therethrough.Subwavelength-scale features (e.g., pillars) may be patterned on thesurface of the substrate to deflect incident optical radiation in acontrolled manner to obtain a target optical radiation output. Such adevice is referred to herein as a metalens. Various embodiments andvariations of metalenses are described herein. Metalenses are broadlydefined herein to encompass both transmissive and reflective devices.Thus, while most of the examples are described in terms of transmissivemetalenses, it is appreciated that many of the embodiments could beimplemented using reflective metalenses, which might be manufactured tobe thinner due to the optical radiation passing through the metasurfaceelements twice.

In some embodiments, subwavelength-scale features may be formed on morethan one surface of the substrate. For example, subwavelength-scalefeatures may be formed on a receiving side of a transmissive substrateand/or an output side of the transmissive substrate. A metalens may beused to deflect optical radiation within free space (e.g., air) or tocouple optical radiation between free space and another transmissivemedium, such as a waveguide, traditional optical lenses, a fiber optictransmission line, or the like.

According to various embodiments, the metalenses described herein may befabricated using any of a wide variety of suitable manufacturingtechniques, including, without limitation nanoimprinting manufacturingtechniques, CMOS fabrication techniques, and/or ultraviolet lithographyprocesses. For example, such processes may be used to fabricate thematerial layers herein that form an array of etchings, holes, gaps,pillars, slots, channels, grooves, or other deflector elements.

In some examples, an optical display device includes a light-emittingdiode (LED), such as a surface mount LED or another type of LED. Thelight-emitting diode may have a planar face from which the opticalradiation is emitted. The planar face may be, for example, a rectangularplanar surface. The light or optical radiation emitted from the planarface may be modeled as having a Lambertian emission profile from a pointsource (e.g., at the center of the rectangular planar surface or as atwo-dimensional array of small point source emitters distributed acrossthe emitting face of the LED). The presently described metalensconfigurations may also be used with LEDs modeled to have non-Lambertianemission profiles.

The LED generates optical radiation within an operational wavelengthband with a divergent emission profile (e.g., a Lambertian emissionprofile) relative to a planar face. A metalens may be positioned tomodify the divergent emission profile of the optical radiation from theLED to have a modified transmission profile. For example, the metalensmay operate to modify the optical radiation from a Lambertian emissionprofile to a condensed, focused, concentrated, or collimated profile.

In various embodiments, the metalens includes a substrate and atwo-dimensional array of passive pillars that extend therefrom withvarying pillar diameters. For example, the metalens may include asubstrate and a two-dimensional array of passive pillars that extendfrom the substrate with a radially symmetric pattern of varying pillardiameters. In other embodiments, the passive pillars may extend from thesubstrate in a disordered array with diameters selected to produce aradially symmetric beam. In still other embodiments, a three-dimensionalnon-periodic structure approximating a volumetric hologram may beutilized. The structures may have high indices of refraction (e.g., n>2,depending on the particular material utilized) and/or low opticalabsorption. The structures may be manufactured using, for example,titanium dioxide, silicon nitride, amorphous silicon, silicon richnitride, hydrogenated silicon rich silicon nitride, and hydrogenatedamorphous silicon (a-H-Silicon), and/or polysilicon. The dimensions ofeach pillar and the subwavelength interelement spacing between adjacentpillars may be selected as a function of the operational wavelength. Thespecific diameters, uniform height, and uniform spacing distance of thepillars create a target phase gradient that modifies the divergentemission profile of the optical radiation from the LED to have themodified transmission profile.

As described herein, the dimensions and operational characteristics ofthe metalens may be varied based on the specific materials used to formthe radially symmetric pattern of pillar diameters. For example,specific dimensions may be selected, as described herein, for passivepillars formed from titanium dioxide. Different dimensions andoperational characteristics can be attached by using polysilicon orother materials.

In various examples, the planar face of the LED is rectangular (e.g.,square), and the metalens is formed to have a corresponding rectangularaperture (e.g., a square aperture). In many embodiments, the thicknessof the metalens may be less than 1.5 millimeters, such as 1 millimeteror less. The metalens may be mounted a few hundred microns from theplanar face of the LED, directly on a window or protective coveringapplied to the planar face of the LED, within a few or tens ofmicrometers, or directly on the planar face of the LED. In someembodiments, an index matching fluid, index matching gel, or indexmatching solid may be used to fill a gap between the metalens and theplanar face of the LED or the window or protective covering on theplanar face of the LED. In some embodiments, as described herein, themetalens may be positioned on or relative to (e.g., mounted to ormanufactured on) the emissive planar face of the LED in an invertedconfiguration in which the passive pillars are in contact with (orminimally spaced from) the planar face of the LED. In such aconfiguration, the passive pillars are positioned between the planarface of the LED and the substrate from which the passive pillars extend.

The aperture of the metalens can be defined as having a radius,regardless of whether the metalens has a circular aperture, a squareaperture, a rectangular aperture, or another aperture shape. In someembodiments, the aperture of a square metalens may be defined in termsof a side length and the aperture of a rectangular metalens may bedefined in terms of the side lengths. In embodiments in which metalensis positioned with a spacing distance or gap between the metalens andthe window layer, the radius or aperture of the metalens is selected asa function of a thickness of the window layer and the spacing distancebetween the metalens and the window layer.

In various embodiments, an optical assembly is formed to include atwo-dimensional array of LEDs. Each LED generates optical radiation atan operational wavelength (e.g., within an operational wavelength band)with a divergent emission profile relative to a planar face thereof. Atwo-dimensional array of metalenses is positioned as a layer to receivethe optical radiation from the two-dimensional array of LEDs. Eachmetalens is positioned relative to one (or more) of the LEDs to modifythe divergent emission profile of the emitted optical radiation to havea modified transmission profile.

In some embodiments, an optical display is manufactured with integratedinverted metalenses or integrated metasurface elements (e.g., pillars),as described in greater detail herein. The optical display may include atwo-dimensional array of LEDs that emit a narrow band of opticalradiation from an emission or planar face with a Lambertian emissionprofile. Each LED includes an integrated metalens in an invertedconfiguration with a two-dimensional array of passive pillars thatextend between the planar face of the LED and a substrate. As previouslydescribed, the passive pillars may be arranged in a radially symmetricpattern of varying pillar diameters, and the diameter of each pillar andinterelement spacings may be selected as a function of an operationalwavelength of the optical radiation emitted by the LED. The integratedinverted metalens functions to provide a target phase gradient thatmodifies the Lambertian emission profile of the optical radiationgenerated by the LED to have a modified transmission profile (e.g.,collimated, condensed, focused, etc.).

The generalized descriptions of the systems and methods herein may beutilized and/or adapted for utilization in a wide variety of industrial,commercial, and personal applications. Similarly, the presentlydescribed systems and methods may be used in conjunction with or utilizeexisting computing devices and infrastructures. Some of theinfrastructure that can be used with embodiments disclosed herein isalready available, such as general-purpose computers, computerprogramming tools and techniques, digital storage media, andcommunication links. A computing device or controller may include aprocessor, such as a microprocessor, a microcontroller, logic circuitry,or the like.

A processor may include one or more special-purpose processing devices,such as application-specific integrated circuits (ASICs), a programmablearray logic (PAL), a programmable logic array (PLA), a programmablelogic device (PLD), a field-programmable gate array (FPGA), or anothercustomizable and/or programmable device. The computing device may alsoinclude a machine-readable storage device, such as non-volatile memory,static RAM, dynamic RAM, ROM, CD-ROM, disk, tape, magnetic, optical,flash memory, or another machine-readable storage medium. Variousaspects of certain embodiments may be implemented using hardware,software, firmware, or a combination thereof.

The components of the disclosed embodiments, as generally described andillustrated in the figures herein, could be arranged and designed in awide variety of different configurations. Furthermore, the features,structures, and operations associated with one embodiment may be appliedto or combined with the features, structures, or operations described inconjunction with another embodiment. In many instances, well-knownstructures, materials, or operations are not shown or described indetail in order to avoid obscuring aspects of this disclosure. Theembodiments of the systems and methods provided within this disclosureare not intended to limit the scope of the disclosure but are merelyrepresentative of possible embodiments. In addition, the steps of amethod do not necessarily need to be executed in any specific order oreven sequentially, nor do the steps need to be executed only once.

FIG. 1A illustrates an example of a light-emitting diode (LED) package100 with a reflector 115 and an aspherical lens 125, according to oneembodiment. In the illustrated embodiment, the reflector is mounted on asubstrate 112. An encapsulation material 120 protects the LED 150 andfills the reflector 115. The aspherical lens 125 may be made of glass,acrylic, or another optically transparent material suitable formanufacturing a refractive lens. As illustrated, the aspherical lens 125may itself have a thickness between 1 and 5 mm, depending on thespecific design of the lens. The reflector 115 may have a thickness ofseveral millimeters or even centimeters, and the substrate 112 may add afew more millimeters to the overall thickness of the LED package 100.

As illustrated, the actual LED 150 may include a substrate 152, a layerof bond metal 154, semiconductor layers 156, and a window layer 158(e.g., glass, sapphire, silicon, etc.). While the LED 150 itself isrelatively thin, the LED package 100, using reflector 115 and/orrefractive optical elements such as the aspherical lens 125, isrelatively thick (e.g., tens of millimeters).

FIG. 1B illustrates a two-dimensional array 175 of LED packages 100 withaspherical lenses 125 to focus the light from underlying LEDs 150,according to one embodiment. As illustrated, the fill factor (or densityor pitch) of the LEDs 150 in the two-dimensional array 175 of LEDpackages 100 is limited by the size of the diameter of the asphericallens 125 required to focus the light from the LED 150. The thickness ofthe two-dimensional array 175 would also be in the tens of millimeters.The use of thinner optical elements, such as microlens arrays, mightreduce the overall thickness of the two-dimensional array 175; however,the effective focal length or the condensing ability of thin opticalelements using traditional refractive properties would be much longerand/or less condensing, respectively, and exhibit significantly moreunwanted spherical aberration.

FIG. 2A illustrates a top-down view of an example representation of apattern of deflector elements 210 for a metalens structure, according toone embodiment. As illustrated, a uniform square grid of deflectorelements 210 may pattern the deflector elements 210 with uniformspacings between adjacent or nearest neighbor deflector elements with upto approximately a 100% fill factor. Moreover, the deflector elements210 may be configured with uniform heights. In the illustrated example,the deflector elements 210 comprise circular pillars arranged in arepeating pattern of pillar diameters.

FIG. 2B illustrates an enlarged perspective view of the examplerepresentation of the pattern of deflector elements in the metalens ofFIG. 2A, according to one embodiment. As illustrated, an array ofdeflector elements 220 includes a uniformly spaced arrangement ofcircular pillars extending from a substrate. The deflector elements 220have different pillar diameters that increase along one dimension (leftto right) and are constant along the other dimension (top to bottom).Alternative patterns of pillar diameters may be used to achieve targetdeflection patterns.

FIG. 3A illustrates an example block diagram of a side view of ametalens 305 with nanopillar deflector elements 330 positioned on asubstrate 350, according to one embodiment. The metalens 305transmissively steers or otherwise phase-modulates incident opticalradiation 371 as deflected optical radiation 376 at a target deflectionangle, beamform, or phase-modulated transmission profile. Asillustrated, the nanopillar deflector elements 330 may have a uniformheight, H, and varying diameters, D. In the illustrated example, thenanopillar deflector elements 330 are evenly spaced with a nearestneighbor on-center spacing distance, P.

The spacing between the centers of adjacent or nearest neighbornanopillars may be constant despite the varying diameters of thepillars. As described herein, the dimensions, pattern, and spacings ofthe nanopillars are selected to achieve a target deflection pattern(e.g., angle of deflection, dispersion, collimation, convergence, and/ora combination thereof) and frequency response (e.g., target operationalbandwidth of optical radiation). The interelement spacing may be on asquare grid or another repeating geometric grid, such as a hexagonalgrid.

FIG. 3B illustrates a metalens 390 with a radially symmetric pattern ofpillar diameters to focus optical radiation, according to oneembodiment. The pattern of diameters to attain a target deflectionpattern can be calculated based on the subwavelength amplitude and phaseresponse of each subwavelength pillar. In some instances, numericalsimulations may be used to determine the pattern of diameters for aparticular deflection pattern (e.g., to focus the optical radiation withan effective focal length). The metalens 390 may be circular, oval,irregularly shaped, or an n-sided polygon, such as a square orrectangle. Expanded window 395 shows an enlarged perspective view of thepassive pillars forming the deflector elements of the metalens. Due tothe limitations of the drawing, the different diameters of the pillarsare not illustrated in the expanded window 395.

The illustrated example is not drawn to scale. For example, a metalensmeasuring four millimeters (4 mm) on each side would include millions oreven hundreds of millions of pillars with varying diameters at uniforminterelement spacings. Rather, the illustrated example is intended tofacilitate the visualization of a possible pattern of radiallysymmetrical and radially repeating pillar diameters. The exact pillardiameters and relative sizes may vary and are based on the results ofphase gradient calculations or simulation results.

Numerical simulations and/or calculations may be used in which theoptical radiation emitted by the LED is modeled in a specific plane Px:y; z as a spherical wave in parabolic approximation. The LED wavefrontcan be modeled as a spherical wave that allows for the determination(calculated or simulated) of a phase gradient or phase profile thatneeds to be imparted to the optical radiation from the LED. Thedetermined phase profile or phase gradient can then be implemented via apattern of pillar diameters. The metalens is manufactured with pillarshaving diameters that correspond to the determined phase gradient (e.g.,phase profile) at each respective spatial location of the metalens. Thespherical wave of the LED can be expressed as:

${{U_{S}\left( {x,y,z} \right)} = {A \cdot {\exp\left( {- {\frac{i\pi}{\lambda z}\left\lbrack {\left( {x_{0} + x} \right)^{2} + \left( {y_{0} + y} \right)^{2}} \right\rbrack}} \right)}}},$

where A is the amplitude, i is the imaginary unit number, A is thewavelength, and z is the distance from the origin Px0; y0; 0. Thesimplified example above is merely representative of one possibleexample approach to determine a phase gradient or phase profile. It isappreciated that any of the various analytical formulas for lenscalculations and holographic techniques may be utilized, as understoodby those of skill in the art. For example, topological optimizationapproaches, such adjoint or inverse design approaches, may be utilizedto determine a distribution of non-periodic structures to achieve atarget optical performance (e.g., modify a divergent emission profile ofoptical radiation from an LED).

FIG. 3C illustrates an example block diagram 300 of a concentrator andcondenser metalens 305 with an LED 380, according to one embodiment. Inthe illustrated embodiment, the LED 380 may be square or rectangular(e.g., 0.5 millimeters×0.5 millimeters on each side) with a thickness ofa few millimeters. The LED 380 may include substrate and semiconductorlayers 381 with an optically transmissive window layer 385. The opticalradiation emitted from the LED 380 may be modeled as being emitted froma point source (e.g., the center of the planar face of the LED 380), ora two-dimensional array of discrete point sources on the planar face ofthe LED 380, with a Lambertian emission profile. The metalens 305 may beless than 2 millimeters thick and, in many instances, may be less than 1millimeter thick (illustrated as less than 1.5 millimeters). Themetalens 305 may have a length and width selected as a function of thedistance between the LED 380 and the metalens 305, which affects howmuch of the emitted light interacts with the metasurface, particularlyat broad angles of emission.

In the illustrated embodiment, the metalens 305 is positionedapproximately 350 micrometers (i.e., 0.350 millimeters) from the LED380. The metalens 305 operates to receive the optical radiation 372emitted with the Lambertian (or other divergent) emission profile andconcentrate and/or condense the optical radiation as output opticalradiation 376 to a spot size with a diameter of approximately 3 mm withan effective focal length of 1.32 millimeters. As described below,simulations of the metalens using titanium dioxide pillars arranged in aradially symmetric pattern allow for optical radiation concentrationefficiencies exceeding 90% (normalized). The example dimensions providedare merely one example of possible dimensions to demonstrate an examplefunctionality of the metalens 305. Additionally, it is readily apparentthat the block diagram 300 is not drawn to scale.

FIG. 4A illustrates an example of a unit cell 400 of a transmissivemetalens for red optical radiation, according to one embodiment. Asillustrated, a titanium dioxide (TiO₂) pillar 407 extends from a silicondioxide (SiO₂) substrate 403. The unit cell 400 is square with a widthof approximately 380 nanometers that corresponds to the on-centerinterelement spacing of an array of unit cells forming a metalens. Thepillar 407, or cylindrical deflector element, extends from the silicondioxide substrate 403 with a height of approximately 600 nanometers. Thesubstrate 403 may, for example, have a thickness of less than 1.5millimeters (e.g., 0.5 millimeters in many embodiments).

A metalens formed to condense red optical radiation may include aradially symmetric pattern of unit cells 400 with pillars 407 that havediameters ranging from approximately 100 nanometers to 320 nanometers(radii ranging from 50 nanometers to 160 nanometers) to attain phaseshifts exceeding a 27 range. In some embodiments, a metalens may bemanufactured with pillar diameters to attain phase shifts less than a 27range. For example, some applications may be adequately served by ametalens with pillar diameters that attain phase shifts within a 0-7range.

FIG. 4B illustrates a graph 480 of the transmission efficiency of redoptical radiation at 624 nanometers (with a 20-30 nanometer bandwidth)for titanium dioxide pillars having radii between approximately 50nanometers and 160 nanometers.

FIG. 4C illustrates a graph 490 of the phase shift of red opticalradiation associated with titanium dioxide pillars having radii betweenapproximately 50 nanometers and 160 nanometers.

FIG. 4D illustrates a finite-difference time-domain (FDTD) simulation495 of a metalens with a radially symmetric pattern of pillar diametersfocusing red optical radiation, according to one embodiment. Due tosimulation limitations, a metalens scaled from 4 mm to 100 micrometerswith a scaled effective focal length of 33 micrometers is simulated,resulting in a spot size of 75 micrometers. According to the simulation,the normalized efficiency is approximately 95%.

FIG. 5A illustrates an example of a unit cell 500 of a transmissivemetalens for green optical radiation, according to one embodiment. Asillustrated, a titanium dioxide (TiO₂) pillar 507 extends from a silicondioxide (SiO₂) substrate 503. The unit cell 500 is square with a widthof approximately 340 nanometers that corresponds to the on-centerinterelement spacing of an array of unit cells 500 forming a metalens.The pillar 507, or cylindrical deflector element, extends from thesilicon dioxide substrate 503 with a height of approximately 600nanometers.

A metalens formed to condense green optical radiation may include aradially symmetric pattern of unit cells 500 with pillars 507 that havediameters ranging from approximately 100 nanometers to 240 nanometers(radii ranging from 50 nanometers to 120 nanometers) to attain phaseshifts exceeding a 2π range.

FIG. 5B illustrates a graph 580 of the transmission efficiency of greenoptical radiation at 522 nanometers (with a 20-30 nanometer bandwidth)for titanium dioxide pillars having radii between approximately 50nanometers and 120 nanometers.

FIG. 5C illustrates a graph 590 of the phase shift of green opticalradiation associated with titanium dioxide pillars having radii betweenapproximately 50 nanometers and 120 nanometers.

FIG. 5D illustrates an FDTD simulation 595 of a metalens with a radiallysymmetric pattern of pillar diameters focusing green optical radiation,according to one embodiment. Again, using a metalens scaled from 4 mm to100 micrometers with a scaled effective focal length of 33 micrometersis simulated, resulting in a spot size of 75 micrometers with anormalized efficiency of approximately 94%.

FIG. 6A illustrates an example of a unit cell 600 of a transmissivemetalens for blue optical radiation, according to one embodiment. Asillustrated, a titanium dioxide (TiO₂) pillar 607 extends from a silicondioxide (SiO₂) substrate 603. The unit cell 600 is square with a widthof approximately 290 nanometers that corresponds to the on-centerinterelement spacing of an array of unit cells 600 forming a metalens.The pillar 607, or cylindrical deflector element, extends from thesilicon dioxide substrate 603 with a height of approximately 600nanometers.

A metalens formed to condense green optical radiation may include aradially symmetric pattern of unit cells 600 with pillars 607 that havediameters ranging from approximately 80 nanometers to 180 nanometers(radii ranging from 40 nanometers to 90 nanometers) to attain phaseshifts exceeding a 2π range.

FIG. 6B illustrates a graph 680 of the transmission efficiency of blueoptical radiation at 455 nanometers (with a 20-30 nanometer bandwidth)for titanium dioxide pillars having radii between approximately 40nanometers and 90 nanometers.

FIG. 6C illustrates a graph 690 of the phase shift of blue opticalradiation associated with titanium dioxide pillars having radii betweenapproximately 40 nanometers and 90 nanometers.

FIG. 6D illustrates an FDTD simulation 695 of a metalens with a radiallysymmetric pattern of pillar diameters focusing blue optical radiation,according to one embodiment. Again, using a metalens scaled from 4 mm to100 micrometers with a scaled effective focal length of 33 micrometersis simulated, resulting in a spot size of 75 micrometers with anormalized efficiency of approximately 93%.

FIG. 7A illustrates a concentrator metalens 705 of titanium dioxidepillars mounted to an LED 780, according to one embodiment. In contrastto the embodiment illustrated and described in conjunction with FIG. 3C,the metalens 705 does not focus the optical radiation to a point.Rather, the metalens 705 operates as a condenser to condense the emittedoptical radiation of a monochrome LED 780. The monochrome LED 780 has adivergent emission profile, such as a Lambertian emission profile. Theoptical radiation 772 transmitted or emitted out of the metalens 705 hasa modified profile that is more condensed or concentrated than theinitial Lambertian emission profile. In some embodiments, the metalens705 includes a distribution of pillars with diameters selected tocondense and/or concentrate as much of the optical radiation as possiblewithin approximately a 30-degree cone.

As previously described, the metalens 705 may comprise a plurality ofpillars arranged in a radially symmetric pattern with diameterscalculated, modeled, or simulated to attain the target deflectionpattern. Pillars formed from titanium dioxide having the ranges ofdiameters described above for the respective wavelengths of LEDs may beutilized to form the metalens 705. The metalens 705 may be mounteddirectly on the protective window 785 of the LED 780, such that thespacing between the planar face of the monochrome LED 780 that emits theoptical radiation and the metalens 705 corresponds not the thickness ofthe window 785 (e.g., a few hundred nanometers or a few microns,depending on the specific LED design). The metalens 705 may haveapproximately the same length and width as the LED 780 or have a largerlength and width than the LED 780 (as illustrated as a square metalenswith a side dimension between approximately 2 millimeters and 3millimeters).

FIG. 7B illustrates an FDTD simulation 781 of a titanium dioxideconcentrator metalens mounted on a red LED, according to one embodiment.As illustrated, the LED-mounted metalens concentrates 94% (normalized)of the 624-nanometer optical radiation within approximately a 30-degreecone.

FIG. 7C illustrates a two-dimensional representation 782 of theoperation of a free space collimator metalens evaluated with red laserlight, according to one embodiment.

FIG. 7D illustrates a graph 784 of the intensity of the free spacecollimator metalens of FIG. 7C, according to one embodiment.

FIG. 7E illustrates a two-dimensional representation 786 of theoperation of a free space collimator metalens evaluated with red laserlight passed through a beam expander, according to one embodiment.

FIG. 7F illustrates a graph 788 of the intensity of the free spacecollimator metalens of FIG. 7E, according to one embodiment.

FIG. 7G illustrates an FDTD simulation 790 of a titanium dioxideconcentrator metalens mounted on a green LED, according to oneembodiment. As illustrated, the LED-mounted metalens concentrates 93%(normalized) of the 522-nanometer optical radiation within approximatelya 30-degree cone.

FIG. 7H illustrates an FDTD simulation 792 of a titanium dioxideconcentrator metalens mounted on a blue LED, according to oneembodiment. As illustrated, the LED-mounted metalens concentrates 91%(normalized) of the 455-nanometer optical radiation within approximatelya 30-degree cone.

FIG. 8A illustrates a condenser metalens 805 of polysilicon (poly-Si)pillars mounted to an LED, according to one embodiment. Again, themetalens 805 operates to condense (e.g., concentrate) the Lambertianemission profile of optical radiation emitted by a monochrome LED 880 sothat the output optical radiation 872 has a modified emission profilethat is more concentrated. The metalens 805 may include a distributionof pillars with diameters selected to condense as much of the opticalradiation as possible within approximately a 30-degree cone. Themetalens 805 may be modified to condense the optical radiation withinwider cone (e.g., a 45-degree cone) or a narrower cone (e.g., a15-degree cone).

As previously described, the metalens 805 may comprise a plurality ofpillars arranged in a radially symmetric pattern with diameterscalculated, modeled, or simulated to attain the target deflectionpattern. Pillars formed from polysilicon having the ranges of diametersdescribed below in conjunction with FIGS. 8B-8D for the respectivewavelengths of LEDs may be utilized to form the metalens 805 that ismounted directly on the LED or placed in very close proximity, such asmounted or fabricated directly on a transparent window 885 of the LED880.

FIG. 8B illustrates an example of a unit cell 800 of a polysiliconconcentrator metalens for red optical radiation, according to oneembodiment. As illustrated, a polysilicon pillar 807 extends from asilicon dioxide (SiO₂) substrate 803. The unit cell 800 is square with awidth of approximately 250 nanometers that corresponds to an exampleon-center interelement spacing of an array of unit cells 800 forming ametalens. The pillar 807, or cylindrical deflector element, extends fromthe silicon dioxide substrate 803 with a height of approximately 250nanometers.

A metalens formed to condense red optical radiation may include aradially symmetric pattern of polysilicon unit cells 800 with pillars807 that have diameters ranging from approximately 80 nanometers to 200nanometers (radii ranging from 40 nanometers to 100 nanometers) toattain phase shifts exceeding a 27 range.

FIG. 8C illustrates a graph 881 of the transmission efficiency of redoptical radiation at 624 nanometers (with a 20-30 nanometer bandwidth)for polysilicon pillars having radii between approximately 40 nanometersand 100 nanometers.

FIG. 8D illustrates a graph 886 of the phase shift of red opticalradiation associated with polysilicon pillars having radii betweenapproximately 40 nanometers and 100 nanometers.

FIG. 8E illustrates an FDTD simulation 891 of a metalens with a radiallysymmetric pattern of polysilicon pillars with diameters selected tocondense red optical radiation, according to one embodiment. Asillustrated, the LED-mounted polysilicon metalens condenses 78%(normalized) of the 624-nanometer optical radiation within a cone. Thepolysilicon metalens uses pillars with a height of 250 nanometers(shorter than the height of 600 nanometers used for the height of thetitanium dioxide pillars) that may result in a thinner metalens.However, according to the simulation, the normalized concentrationefficiency of the polysilicon metalens (78%) is lower than thenormalized concentration efficiency of the simulated titanium dioxidemetalens (compare with FIG. 7B).

FIG. 8F illustrates an example of a unit cell 801 of a polysiliconconcentrator metalens for green optical radiation, according to oneembodiment. As illustrated, a polysilicon pillar 808 extends from asilicon dioxide (SiO₂) substrate 804. The unit cell 801 is square with awidth of approximately 190 nanometers, which corresponds to an exampleon-center interelement spacing of an array of unit cells 801 forming ametalens. The pillar 808, or cylindrical deflector element, extends fromthe silicon dioxide substrate 804 with a height of approximately 250nanometers.

A metalens formed to condense green optical radiation may include aradially symmetric pattern of polysilicon unit cells 801 with pillars808 that have diameters ranging from approximately 80 nanometers to 170nanometers (radii ranging from 40 nanometers to 85 nanometers) to attainphase shifts exceeding a 27 range.

FIG. 8G illustrates a graph 882 of the transmission efficiency of greenoptical radiation at 522 nanometers (with a 20-30 nanometer bandwidth)for polysilicon pillars having radii between approximately 40 nanometersand 85 nanometers.

FIG. 8H illustrates a graph 887 of the phase shift of green opticalradiation associated with polysilicon pillars having radii betweenapproximately 40 nanometers and nanometers.

FIG. 8I illustrates an FDTD simulation 892 of concentrated green opticalradiation by a metalens with polysilicon pillars mounted to a green LED,according to one embodiment. As illustrated, the LED-mounted polysiliconmetalens concentrates 64% (normalized) of the 522-nanometer opticalradiation within approximately a 30-degree cone.

FIG. 8J illustrates an example of a unit cell 802 of a polysiliconconcentrator metalens for blue optical radiation, according to oneembodiment. As illustrated, a polysilicon pillar 809 extends from asilicon dioxide (SiO₂) substrate 806. The unit cell 802 is square with awidth of approximately 180 nanometers that corresponds to an exampleon-center interelement spacing of an array of unit cells 802 forming ametalens. The pillar 809, or cylindrical deflector element, extends fromthe silicon dioxide substrate 806 with a height of approximately 250nanometers.

A metalens formed to condense blue optical radiation may include aradially symmetric pattern of polysilicon unit cells 802 with pillars809 that have diameters ranging from approximately 80 nanometers to 170nanometers (radii ranging from 40 nanometers to 85 nanometers) to attainphase shifts exceeding a 2π range.

FIG. 8K illustrates a graph 883 of the transmission efficiency of blueoptical radiation at 455 nanometers (with a 20-30 nanometer bandwidth)for polysilicon pillars having radii between approximately 40 nanometersand 85 nanometers.

FIG. 8L illustrates a graph 888 of the phase shift of blue opticalradiation associated with polysilicon pillars having radii betweenapproximately 40 nanometers and nanometers.

FIG. 8M illustrates an FDTD simulation 893 of concentrated blue opticalradiation by a metalens with polysilicon pillars mounted to a blue LED,according to one embodiment. As illustrated, the LED-mounted polysiliconmetalens concentrates 38% (normalized) of the 455-nanometer opticalradiation within approximately a 30-degree cone.

FIG. 9A illustrates an example LED corrector metalens 980 with aradially symmetric pattern of pillar diameters, according to oneembodiment. The LED corrector metalens 980 may be paired with anunderlying LED that emits optical radiation with a divergent emissionprofile (e.g., such as a Lambertian emission profile, butterfly wingemission profile, batwing emission profile, uniform low angle emissionprofile, uniform broad angle emission profile, elliptical emissionprofile, etc.). The corrector metalens 980 may operate to, for example,receive the optical radiation emitted by the underlying LED with thedivergent emission profile and operate to modify the optical radiationto have a modified transmission profile. As such, the optical radiationemitted from the metalens has a modified transmission profile that maybe, for example, a collimated transmission profile, a concentratedtransmission profile, a condensed transmission profile, a widertransmission profile, a more uniform transmission profile, a split beamtransmission profile, and/or a combination thereof. As described herein,the pillars or other deflector elements forming the metalens may bemanufactured using titanium dioxide, polysilicon, amorphous silicon,hydrogenated amorphous silicon (a-H-Silicon), silicon nitride, siliconrich nitride, hydrogenated silicon rich nitride, and/or a combinationthereof.

FIG. 9B illustrates a graph 982 of the energy focus for red opticalradiation using titanium dioxide pillars, according to one embodiment.

FIG. 9C illustrates a graph 984 of the energy focus for red opticalradiation using polysilicon pillars, according to one embodiment.

FIG. 10A illustrates a block diagram of an LED 1080 with planar face1082 from which optical radiation 1085 is emitted with a Lambertianemission profile, as exemplified by graph 1086.

FIG. 10B illustrates a block diagram of the LED 1080 with a metalens1005 positioned in planar alignment with planar face 1082 of the LED1080. The metalens 1005 is configured to collimate and/or condense theoptical radiation from the LED 1080 into a modified transmission profile1095. The graph 1096 illustrates an example modified transmissionprofile.

FIG. 11A illustrates a block diagram of a metalens 1105 for an LED 1180,according to one embodiment. As illustrated and described in conjunctionwith other embodiments, the metalens 1105 includes a substrate 1150 anda two-dimensional array of passive pillars 1130 that extend from thesubstrate away from the LED 1180. In the illustrated view, only a singleline of the passive pillars 1130 is visible. However, it is understoodthat the metalens 1105 may be circular, rectangular, square, have anirregular shape, or be an N-sided polygon. The two-dimensional array ofpassive pillars 1130 extends from the substrate with a repeating patternof varying diameters and on-center spacings to create a target phasegradient for an operational bandwidth. An example of a linearlysymmetric pattern of pillar diameters with uniform on-centerinterelement spacing (subwavelength) is illustrated in FIG. 2B. Anexample of a radially symmetric pattern of pillar diameters withuniform, subwavelength, on-center interelement spacing is illustratedand described in conjunction with FIGS. 15A-15D.

As illustrated, the LED 1180 has an integrated window layer 1185 thatoperates to protect the LED and/or modify the emission profile of theoptical radiation generated by the LED 1180. The optical radiationemitted from the surface of the LED 1180 and/or from the surface of thewindow layer 1185 may be approximated as a Lambertian emission profileor another divergent emission profile. The metalens 1105 may bepositioned directly on the window layer 1185 in a standard configurationin which the substrate 1150 is positioned (e.g., mounted, fused, glued,connected, mechanically secured, etc.) adjacent to the window layer1185. As such, the optical radiation from the LED 1180 travels throughthe window layer 1185 and the (transparent or transmissive) substrate1150 before being modified by the passive pillars 1130 of themetasurface comprising the two-dimensional array of passive pillars. Thetwo-dimensional array of passive pillars may, for example, include aradially symmetric pattern of varying pillar diameters. The combinationof the LED 1180 and the metalens 1105 may be used as or referred to asan optical assembly or optical device 1100.

The diameter of each individual pillar is selected as a function of theoperational wavelength or wavelength band of the LED 1180 (e.g., arelatively narrow bandwidth from a monochrome LED) such that the passivepillars 1130 of the metasurface provide a target phase gradient (atwo-dimensional phase gradient) on the surface of the substrate 1150.The two-dimensional phase gradient formed by the passive pillars 1130 ofthe metasurface operates to modify the divergent emission profile of theoptical radiation from the LED 1180 to have a modified transmissionprofile. Optical radiation 1195 with the modified transmission profileis emitted or transmitted that may have, for example, a condensedprofile, a collimated profile, a concentrated profile, a focusedprofile, etc.

FIG. 11B illustrates geometric calculations associated with the metalensof FIG. 11A, according to one embodiment. As illustrated, opticalradiation from the LED 1180 is emitted through the window layer (notshown) and the substrate 1150 before passing through the passive pillars1130. The passive pillars 1130 modify the incident optical radiation tohave a modified transmission profile with a modified angle ofdivergence, θ_(m), from a centerline. Calculations 1125 illustrate thecalculation of the radius of the metasurface, r_(M), as a function ofthe radius of the planar emitting face, r_(L), of the LED 1180, themaximum angle of divergence, θL, of the optical radiation emitted by theLED 1180 that will interact with the metasurface, and the total distancebetween the planar emitting face, r_(L), of the LED 1180 and themetasurface of the metalens. The total distance between the planaremitting face, r_(L), of the LED 1180 and the metasurface of themetalens is equal to the sum of the thickness of the substrate, t_(s),and the gap, δ, between the LED 1180 and the substrate 1150. In theembodiment illustrated in FIG. 11A, where the substrate 1150 is mounteddirectly to the window layer 1185, the total distance between the planaremitting face, r_(L), of the LED 1180 and the metasurface of themetalens is equal to the sum of the thickness of the substrate, t_(s),and the thickness of the window layer 1185.

FIG. 11C illustrates a table 1127 of example metasurface radius values,r_(M), calculated for various angles of divergence values, θ_(L), for anLED having a radius of 0.25 millimeters. As illustrated, the thicknessof the substrate, t_(s), (0.5 mm) and the thickness of window layer, δ,(0.1 mm) have a significant impact on the radius of the metasurface,r_(M). As illustrated, even for a 70° maximum angle of divergence, theradius of the metasurface, r_(M), is more than 7.5 times as large as theradius of the LED, r_(L). With an 85° maximum angle of divergence, theradius of the metasurface, r_(M), is more than 28 times as large as theradius of the LED, r_(L).

FIG. 12A illustrates a block diagram of an inverted metalens 1205 for anLED, according to one embodiment. As illustrated and described inconjunction with other embodiments, the metalens 1205 includes asubstrate 1250 and a two-dimensional array of passive pillars 1230 thatextend from the substrate. Again, the metalens 1205 may be circular,rectangular, square, have an irregular shape, or be an N-sided polygon.The two-dimensional array of passive pillars 1230 extends from thesubstrate with a repeating pattern of varying diameters and on-centerspacings to create a target phase gradient for an operational bandwidth.

As illustrated, the LED 1280 has an integrated window layer 1285 thatoperates to protect the LED and/or modify the emission profile of theoptical radiation generated by the LED 1180. The optical radiationemitted from the surface of the LED 1280 and/or from the surface of thewindow layer 1285 may be approximated as a Lambertian emission profileor another divergent emission profile. The metalens 1105 may bepositioned directly on the window layer 1285 in an invertedconfiguration in which the metasurface of passive pillars 1230 ispositioned (e.g., mounted, fused, glued, connected, mechanicallysecured, etc.) adjacent to the window layer 1285. As such, the opticalradiation from the LED 1180 travels through the window layer 1285, ismodified by the metasurface of passive pillars 1230 and then passesthrough the (transparent or transmissive) substrate 1250. Thetwo-dimensional array of passive pillars 1230 may, for example, includea radially symmetric pattern of varying pillar diameters. Thecombination of the LED 1280 and the metalens 1205 may be used as orreferred to as an optical assembly or optical device 1200.

The diameter of each individual pillar is selected as a function of theoperational wavelength of the LED 1280 (e.g., a narrow bandwidth from amonochrome LED) such that the metasurface of passive pillars 1230provide a target phase gradient (a two-dimensional phase gradient) onthe surface of the substrate 1250. The two-dimensional phase gradientformed by the passive pillars 1230 of the metasurface operates to modifythe divergent emission profile of the optical radiation from the LED1280 to have a modified transmission profile. Optical radiation 1295with the modified transmission profile is emitted or transmitted thatmay have, for example, a condensed profile, a collimated profile, aconcentrated profile, a focused profile, one or more deflected beams,etc.

FIG. 12B illustrates geometric calculations associated with the invertedmetalens of FIG. 11A, according to one embodiment. As illustrated,optical radiation from the LED 1180 is emitted through the gap or windowlayer (not shown) before passing through the passive pillars 1230. Thepassive pillars 1230 modify the incident optical radiation to have amodified transmission profile with a modified angle of divergence,θ_(m), from a centerline. The optical radiation is modified by thepassive pillars 1230 before passing through the substrate 1250.Calculations 1225 illustrate the calculation of the radius of themetasurface, r_(M), as a function of the radius of the planar emittingface, r_(L), of the LED 1280, the maximum angle of divergence, θ_(L), ofthe optical radiation emitted by the LED 1280 that will interact withthe metasurface, and the total distance between the planar emittingface, r_(L), of the LED 1280 and the metasurface. In the invertedconfiguration, the total distance between the planar emitting face,r_(L), of the LED 1280 and the metasurface is equal to the thickness ofthe window layer and/or any gap, δ, between the LED 1280 and themetasurface. The thickness of the substrate is not a factor in theinverted configuration. In the embodiment illustrated in FIG. 12A, wherethe passive pillars 1230 are mounted directly to the window layer 1285,the total distance between the planar emitting face, r_(L), of the LED1280 and the metasurface (e.g., the passive pillars 1230) is equal tothe thickness of the window layer 1285.

FIG. 12C illustrates a table 1227 of example inverted metasurface radiusvalues, r_(M), calculated for various angles of divergence values,θ_(L), for an LED having a radius of 0.25 millimeters. As illustrated,the thickness of the substrate, t_(s), (0.5 mm) is not a factor. Thethickness of window layer, δ, (0.1 mm) impacts the radius of themetasurface, r_(M). As illustrated, for a 70° maximum angle ofdivergence, the radius of the metasurface, r_(M), is approximately twotimes as large as the radius of the LED, r_(L). With an maximum angle ofdivergence, the radius of the metasurface, r_(M), is approximately 5.5times as large as the radius of the LED, r_(L). Decreasing the thicknessof the window and/or removing the window layer can significantlydecrease the relative size of the radius of the metasurface compared tothe radius of the LED when the metalens is positioned in the invertedconfiguration.

FIG. 13A illustrates a block diagram of an LED 1380 with an invertedmetalens with the metasurface of passive pillars 1330 applied to an LEDsurface, according to one embodiment. As illustrated, optical radiationfrom the LED 1380 is emitted with a divergent emission profile directlyinto the passive pillars 1330. In some embodiments, there is no gapbetween the passive pillars 1330 and the planar surface of the LED 1380.In other embodiments, a gap between 0 and 50 micrometers (0.05millimeters) may be used to prevent damage to the passive pillars 1330during positioning. In some embodiments, the passive pillars 1330 areencapsulated in a transparent medium, such as an optical adhesive tobond the metasurface elements (the passive pillars 1330) to the LED1380. In some embodiments, the passive pillars 1330 may be manufactureddirectly on the top layer of the LED 1380. In some of the embodiments inwhich the passive pillars 1330 are manufactured directly on the toplayer of the LED, the top layer of the LED 1380 serves as the“substrate” for the metalens, and the substrate 1350 may be omitted.

In the various embodiments described herein, the passive pillars 1330modify the optical radiation 1395 to have a modified transmissionprofile. The optical radiation from the LED 1380 is modified by thepassive pillars 1330 before passing through the substrate 1350. Usingthe same calculations used in conjunction with FIGS. 12B and 12C, a gapof 50 microns allows for an inverted metasurface radius value, r_(M), of0.38 mm for a 70° angle of divergence (1.5 times the radius of the LED),or 0.82 mm for an 85° angle of divergence (3.3 times the radius of theLED).

FIG. 13B illustrates a two-dimensional array 1375 of LEDs with invertedmetalenses, according to one embodiment. As compared to FIG. 1B, the useof an inverted metalens mounted directly on the planar surface of theLED, even with a very small gap (<100 microns), allows for a much higherfill factor of the metalenses with respect to the LEDs.

FIG. 14A illustrates a block diagram of an LED 1480 with an invertedmetalens with a matched aperture applied to a planar surface of the LED1480, according to one embodiment. Optical radiation from the LED 1480is emitted with a divergent emission profile directly into the passivepillars 1430 for conversion to optical radiation 1495 with a modifiedtransmission/emission profile. There is no gap between the planarsurface of the LED 1480 and the passive pillars 1430. In someembodiments, the substrate 1450 may still be present as part of themetalens, and the passive pillars 1430 extend therefrom toward theplanar surface of the LED 1480. In other embodiments, the passivepillars 1430 may be manufactured directly on the top layer of the LED1480, such that the top layer of the LED 1480 serves as the “substrate”for the metalens and the substrate 1450 is omitted or acts as aprotective or stabilizing window or covering.

In the various embodiments described herein, the passive pillars 1330modify the optical radiation 1395 to have a modified transmissionprofile. The optical radiation from the LED 1380 is modified by thepassive pillars 1330 before passing through the substrate 1350. Usingthe same calculations used in conjunction with FIGS. 12B and 12C, a gapof 50 microns allows for an inverted metasurface radius value, r_(M), of0.38 mm to interact with light at a maximum 70° angle of divergence (1.5times the radius of the LED), or 0.82 mm for an 85° angle of divergence(3.3 times the radius of the LED).

FIG. 14B illustrates a two-dimensional array 1475 of LEDs withmatched-aperture inverted metalenses, according to one embodiment. Ascompared to FIG. 1B, and even as compared to FIG. 13B, the use of aninverted metalens with a gapless mounting directly on the planar surfaceof the LED allows for a much higher fill factor of the metalenses withrespect to the LEDs. The density of the LEDs, pitch spacing, or fillfactor is not limited by the metalens and is instead determined by thesize of the LEDs, the LED manufacturing process, any associatedco-planar wiring (if any), and/or associated co-planar heat sinks (ifany).

FIGS. 15A-D illustrate images of the arrays of pillars forming ametalens captured using an electronic microscope at varying levels ofmagnification, according to various embodiments. FIG. 15A illustrates animage 1591 of an example metalens 1500 with a radially symmetric patternof deflector elements (passive pillars). The diameter of the metalens1500 is approximately 1 millimeter. The illustrated metalens 1500 iscircular in shape. In alternative embodiments, the metalens may berectangular, square, a hexagon, or another shape, as described herein.

FIG. 15B illustrates an image 1592 of the metalens 1500 magnifiedapproximately 50× more than the image 1591 in FIG. 15A to show theradially symmetric pattern of the varying diameters of the passivepillars forming the metasurface of the metalens. As described herein,the passive pillars forming the metasurface may be manufactured on asubstrate of the metalens.

FIG. 15C illustrates an image 1592 of the metalens 1500 magnified anadditional 2.5× to show the varying diameters of the individual passivepillars arranged in repeating patterns of increasing diameters in anoverall radially symmetric pattern.

FIG. 15D illustrates an image 1593 of a small section of the metalens1500 magnified an addition 4× to show the circular tops of the passivepillars and their varying diameters. As illustrated, a uniformsubwavelength interelement spacing is used between adjacent pillars inthe radially symmetric pattern. The passive pillars are illustrated ashaving a circular cross-section, such that the passive pillars can bedescribed as cylinders that extend from the substrate. In alternativeembodiments, the passive pillars may have oval cross sections,rectangular (e.g., square) cross sections, hexagonal cross sections, orother irregular or N-sided polygonal cross sections. The illustratedexample shows the diameters of the passive pillars increasing fromsmallest to largest in a repeating radial pattern from the center to theedge of the metalens 1500. It is appreciated that for the metasurface toform a target phase gradient to modify a divergent emission profile ofinput optical radiation to have a modified transmission profile, thespecific diameters and the radially repeated patterns of diameters maybe varied and modified from the illustrated example. Thus, the patternof passive pillar diameters may not be uniform from smallest to largest,as illustrated in the example metalens 1500 in image 1593.

In some embodiments, the nanopillars (also referred to herein as simply“pillars” or “passive pillars”) may be arranged in rows and columns,concentric rings, radially but without overall radial symmetry, and/orin other patterns to achieve a target phase gradient. In variousembodiments, the metalens is polarization-independent as the passivepillars are themselves polarization-independent.

This disclosure has been made with reference to various embodiments,including the best mode. However, those skilled in the art willrecognize that changes and modifications may be made to the variousembodiments without departing from the scope of the present disclosure.While the principles of this disclosure have been shown in variousembodiments, many modifications of structure, arrangements, proportions,elements, materials, and components may be adapted for a specificenvironment and/or operating requirements without departing from theprinciples and scope of this disclosure. These and other changes ormodifications are intended to be included within the scope of thepresent disclosure as encompassed by the claims below, which form a partof this disclosure.

What is claimed is:
 1. An optical device, comprising: a light-emittingdiode (LED) to generate optical radiation at an operational wavelengthwith a Lambertian emission profile relative to a planar face thereof;and a metalens positioned to modify the Lambertian emission profile ofthe optical radiation from the LED to have a modified transmissionprofile, the metalens comprising: a substrate, and a two-dimensionalarray of passive pillars that extend from the substrate with varyingpillar diameters, wherein a diameter of each pillar and a subwavelengthinterelement spacing between adjacent pillars are selected functions ofthe operational wavelength to provide a target phase gradient thatmodifies a divergent emission profile of the optical radiation from theLED to have the modified transmission profile, and wherein the LED isconfigured to generate the optical radiation with a Lambertian emissionprofile relative to the planar face.
 2. The device of claim 1, whereinthe diameters and interelement spacing of the two-dimensional array ofpassive pillars are selected to condense the optical radiation from theLED.
 3. The device of claim 1, wherein each of the passive pillarscomprises at least one of: polysilicon, titanium dioxide, siliconnitride, amorphous silicon, silicon rich nitride, hydrogenated siliconrich silicon nitride, and hydrogenated amorphous silicon (a-H-Silicon).4. The device of claim 1, wherein the passive pillars extend from thesubstrate with a non-periodic distribution of pillars having varyingdiameters.
 5. The device of claim 1, further comprising a window layeron the planar face of the LED positioned between the LED and themetalens.
 6. The device of claim 5, wherein the metalens is mounteddirectly to the window layer.
 7. The device of claim 6, wherein thesubstrate of the metalens is mounted directly to the window layer, suchthat the passive pillars extend from the substrate away from the LED,and wherein a radius of the metalens corresponds to a radius of theplanar face of the LED, scaled larger as a function of a thickness ofthe window layer and the thickness of the substrate.
 8. The device ofclaim 6, wherein the metalens is mounted inverted with the passivepillars between the substrate and the window layer, such that thepassive pillars extend from the substrate toward the LED, and wherein aradius of the metalens corresponds to the radius of the planar face ofthe LED, scaled as a function of a thickness of the window layer.
 9. Thedevice of claim 5, wherein the metalens is positioned with a spacingdistance between the metalens and the window layer, and wherein a radiusof the metalens is selected as a function of a thickness of the windowlayer and the spacing distance between the metalens and the windowlayer.
 10. The device of claim 9, wherein the planar face of the LED issquare with a radius of approximately 0.25 millimeters, wherein themetalens is square with a radius of approximately 2 millimeters and athickness less than 1 millimeter, and wherein the spacing distancebetween the metalens and the window layer is approximately 350micrometers.
 11. The device of claim 1, wherein the passive pillarsextend from the substrate with a radially symmetric pattern of varyingpillar diameters.
 12. The device of claim 1, wherein the metalens ismounted inverted with the passive pillars between the substrate and theplanar face of the LED, such that the passive pillars extend from thesubstrate toward the planar face of the LED.
 13. An optical device,comprising: a light-emitting diode (LED) to generate optical radiationat an operational wavelength with a Lambertian emission profile relativeto a planar face thereof; and a metalens positioned to modify theLambertian emission profile of the optical radiation from the LED tohave a modified transmission profile, the metalens comprising: asubstrate, and a two-dimensional array of passive pillars that extendfrom the substrate with varying pillar diameters, wherein a diameter ofeach pillar and a subwavelength interelement spacing between adjacentpillars are selected as functions of the operational wavelength toprovide a target phase gradient that modifies a divergent emissionprofile of the optical radiation from the LED to have the modifiedtransmission profile, wherein the passive pillars extend from thesubstrate with a radially symmetric pattern of varying pillar diameters.14. The device of claim 13, wherein the modified transmission profilecomprises a collimated transmission profile, and wherein the diametersand interelement spacing of the two-dimensional array of passive pillarsare selected to collimate the optical radiation from the LED.
 15. Thedevice of claim 13, wherein the diameters and interelement spacing ofthe two-dimensional array of passive pillars are selected to condensethe optical radiation from the LED.
 16. The device of claim 13, whereinthe passive pillars extend from the substrate with a non-periodicdistribution of pillars having varying diameters.
 17. The device ofclaim 13, further comprising a window layer on the planar face of theLED positioned between the LED and the metalens, wherein the metalens ismounted directly to the window layer, wherein the substrate of themetalens is mounted directly to the window layer, such that the passivepillars extend from the substrate away from the LED, and wherein aradius of the metalens corresponds to a radius of the planar face of theLED, scaled larger as a function of a thickness of the window layer andthe thickness of the substrate.
 18. The device of claim 13, furthercomprising a window layer on the planar face of the LED positionedbetween the LED and the metalens, wherein the metalens is mounteddirectly to the window layer, wherein the metalens is mounted invertedwith the passive pillars between the substrate and the window layer,such that the passive pillars extend from the substrate toward the LED,and wherein a radius of the metalens corresponds to the radius of theplanar face of the LED, scaled as a function of a thickness of thewindow layer.
 19. The device of claim 13, wherein the metalens ismounted inverted with the passive pillars between the substrate and theplanar face of the LED, such that the passive pillars extend from thesubstrate toward the planar face of the LED.
 20. An optical device,comprising: a light-emitting diode (LED) to generate optical radiationat an operational wavelength with a Lambertian emission profile relativeto a planar face thereof; and a metalens positioned to modify theLambertian emission profile of the optical radiation from the LED tohave a modified transmission profile, the metalens comprising: asubstrate, and a two-dimensional array of passive pillars that extendfrom the substrate with varying pillar diameters, wherein a diameter ofeach pillar and a subwavelength interelement spacing between adjacentpillars are selected functions of the operational wavelength to providea target phase gradient that modifies a divergent emission profile ofthe optical radiation from the LED to have the modified transmissionprofile, wherein the planar face of the LED is rectangular and whereinthe metalens has a rectangular aperture with a thickness of less than 1millimeter.
 21. The device of claim 20, wherein the LED is configured togenerate the optical radiation with a Lambertian emission profilerelative to the planar face.
 22. The device of claim 20, wherein thediameters and interelement spacing of the two-dimensional array ofpassive pillars are selected to condense the optical radiation from theLED.
 23. The device of claim 20, wherein the modified transmissionprofile comprises a collimated transmission profile, and wherein thediameters and interelement spacing of the two-dimensional array ofpassive pillars are selected to collimate the optical radiation from theLED.
 24. The device of claim 20, wherein the passive pillars extend fromthe substrate with a non-periodic distribution of pillars having varyingdiameters.
 25. The device of claim 20, wherein the passive pillarsextend from the substrate with a radially symmetric pattern of varyingpillar diameters.
 26. The device of claim 20, further comprising awindow layer on the planar face of the LED positioned between the LEDand the metalens, wherein the metalens is mounted directly to the windowlayer, wherein the substrate of the metalens is mounted directly to thewindow layer, such that the passive pillars extend from the substrateaway from the LED, and wherein a radius of the metalens corresponds to aradius of the planar face of the LED, scaled larger as a function of athickness of the window layer and the thickness of the substrate. 27.The device of claim 20, further comprising a window layer on the planarface of the LED positioned between the LED and the metalens, wherein themetalens is mounted directly to the window layer, wherein the metalensis mounted inverted with the passive pillars between the substrate andthe window layer, such that the passive pillars extend from thesubstrate toward the LED, and wherein a radius of the metalenscorresponds to the radius of the planar face of the LED, scaled as afunction of a thickness of the window layer.
 28. The device of claim 20,wherein the metalens is mounted inverted with the passive pillarsbetween the substrate and the planar face of the LED, such that thepassive pillars extend from the substrate toward the planar face of theLED.
 29. The device of claim 20, wherein the metalens is mountedinverted with the passive pillars between the substrate and the planarface of the LED, such that the passive pillars extend from the substratetoward the planar face of the LED.
 30. An optical device, comprising: alight-emitting diode (LED) to generate optical radiation at anoperational wavelength with a Lambertian emission profile relative to aplanar face thereof; and a metalens positioned to modify the Lambertianemission profile of the optical radiation from the LED to have amodified transmission profile, the metalens comprising: a substrate, anda two-dimensional array of passive pillars that extend from thesubstrate with varying pillar diameters, wherein a diameter of eachpillar and a subwavelength interelement spacing between adjacent pillarsare selected as functions of the operational wavelength to provide atarget phase gradient that modifies a divergent emission profile of theoptical radiation from the LED to have the modified transmissionprofile, wherein the metalens is mounted inverted with the passivepillars between the substrate and the planar face of the LED, such thatthe passive pillars extend from the substrate toward the planar face ofthe LED with a gap of less than 50 micrometers, wherein a radius of themetalens is equal to or greater than a radius of the planar face of theLED, and wherein a thickness of the substrate is less than 1 millimeter.31. The device of claim 30, wherein the planar face of the LED issquare, and wherein the metalens is square.
 32. The device of claim 30,wherein the LED is configured to generate the optical radiation with aLambertian emission profile relative to the planar face.
 33. The deviceof claim 30, wherein the diameters and interelement spacing of thetwo-dimensional array of passive pillars are selected to condense theoptical radiation from the LED.
 34. The device of claim 30, wherein themodified transmission profile comprises a collimated transmissionprofile, and wherein the diameters and interelement spacing of thetwo-dimensional array of passive pillars are selected to collimate theoptical radiation from the LED.
 35. The device of claim 30, wherein thepassive pillars extend from the substrate with a non-periodicdistribution of pillars having varying diameters.
 36. The device ofclaim 30, wherein the passive pillars extend from the substrate with aradially symmetric pattern of varying pillar diameters.
 37. An opticalsystem, comprising: a two-dimensional array of light-emitting diodes(LEDs), wherein each LED is configured to emit optical radiation at anoperational wavelength with a divergent emission profile relative to aplanar face thereof; and a two-dimensional array of metalensespositioned as a layer to receive optical radiation from thetwo-dimensional array of LEDs, wherein each metalens is positionedrelative to one of the LEDs to modify the divergent emission profile ofthe emitted optical radiation to have a modified transmission profile,wherein each metalens comprises a two-dimensional array of passivepillars that extend from a substrate with a radially symmetric patternof varying pillar diameters, and wherein a diameter of each pillar and asubwavelength interelement spacing between adjacent pillars are selectedas functions of the operational wavelength of an associated LED toprovide a target phase gradient that modifies the divergent emissionprofile of the emitted optical radiation to have the modifiedtransmission profile.
 38. The system of claim 37, wherein each LED isconfigured to generate optical radiation with a Lambertian emissionprofile.
 39. The system of claim 37, wherein the modified transmissionprofile comprises one of a collimated transmission profile and acondensed transmission profile.
 40. The system of claim 37, wherein eachof the passive pillars of each metalens is formed from at least one of:titanium dioxide, silicon nitride, amorphous silicon, silicon richnitride, hydrogenated silicon rich silicon nitride, hydrogenatedamorphous silicon (a-H-Silicon), and polysilicon.
 41. The system ofclaim 37, wherein the metalens is mounted inverted with the passivepillars between the substrate and the planar face of the LED.
 42. Thesystem of claim 37, wherein each LED comprises a window layer positionedbetween the planar face and the associated metalens, and wherein themetalens is mounted directly to the window layer.
 43. The system ofclaim 42, wherein the substrate of each metalens is mounted directly tothe window layer of a corresponding LED, such that the passive pillarsof each respective metalens extend from the substrate away from theassociated LED.
 44. The system of claim 42, wherein each metalens ismounted inverted with passive pillars between the substrate and thewindow layer of an associated LED, such that the passive pillars of eachrespective metalens extend from the substrate toward the associated LED.45. The system of claim 37, wherein each LED in a first subset of theLEDs is configured to emit optical radiation within a first operationalbandwidth and each LED in a second subset of the LEDs are configured toemit optical radiation within a second operational bandwidth.
 46. Anoptical display with integrated inverted metalenses, comprising: atwo-dimensional array of light-emitting diodes (LEDs), wherein each LEDcomprises: a planar face to emit optical radiation with a Lambertianemission profile; and an integrated metalens in an invertedconfiguration with a two-dimensional array of passive pillars thatextend between the planar face of the LED and a substrate, wherein thepassive pillars are arranged in a radially symmetric pattern of varyingpillar diameters, wherein the diameter of each pillar and asubwavelength interelement spacing between adjacent pillars are selectedas functions of an operational wavelength of the optical radiationemitted by the LED to provide a target phase gradient that modifies theLambertian emission profile of the optical radiation generated by theLED to have a modified transmission profile.
 47. The optical display ofclaim 46, wherein the modified transmission profile comprises one of acollimated transmission profile, a condensed transmission profile, and afocused transmission profile with a target focus length.
 48. The opticaldisplay of claim 46, wherein each of the passive pillars comprises oneof: titanium dioxide, silicon nitride, amorphous silicon, silicon richnitride, hydrogenated silicon rich silicon nitride, hydrogenatedamorphous silicon (a-H-Silicon), and polysilicon.